In a deep pot, heat milk, cream, polenta, thyme, and Parmesan. Bring to a boil, then cook over medium heat, stirring for 10 minutes until thick and stable. Transfer the polenta to a 20x30 cm (8x12 inch) baking dish lined with parchment paper, spreading it out evenly. The dish should be shallow, about 1-2 cm (0.4-0.8 inches) deep. Cover with plastic wrap, pressing the wrap onto the polenta, and refrigerate for at least 2 hours or overnight.

Remove the polenta from the refrigerator and cut into 2x10 cm (0.8x4 inch) rectangles.

Heat oil in a deep pot, coat each chip in polenta flour, and fry on both sides until golden brown. Remove to a wire rack or paper towel.

Cut the mushrooms into quarters and sear them in a dry pan, then season with a little salt.

In a pan, melt butter and cooking cream, gradually adding Parmesan and cooking just until it bubbles. Add extra Parmesan if desired.

On a serving plate, pour the Parmesan cream. Place the polenta chips on top of the cream. Add the seared mushrooms and sprinkle with grated Parmesan. Garnish with arugula.

Notes:

Use coarse polenta rather than instant. Chips and sauce can be served separately; reheat everything before serving. Can be served with any sauce you like: tomato, pesto, etc. Polenta can be stored in the refrigerator for up to two days, wrapped in plastic wrap.